Basically, each LI has multiple paths, some two paths, some three paths, some four paths. Those paths being - Slut, Sub, Mistress, Girlfriend. Only a few characters have the "Girlfriend" path, most of them can be your sub or mistress for now, although I wouldn't be surprised if the number of girlfriends you can have will raise later on. Then of course there's the slut path, which I personally just don't care for, but if there's a character you don't like and you want to make her into a slut, there's always the option.
Some paths branch off further with certain characters, like sharing with Lois for example on the slut/whore or sub paths. There's no sharing content with Lois on the sub path yet that I'm aware of anyways, but there will be in the future. You can also combine some paths, like Lois can be your girlfriend and your sub for example, you'll maintain the sub relationship with her, while also being loving to her and she will soon be living with the MC as well if she's the MC's girlfriend.
Kari is the main love interest of the game, so she doesn't have a mistress path, but she can also be made into a slut if you want, I can't remember if she has a sub path or not, and she can of course be your girlfriend.
I won't go through all the characters, it's definitely not a generic harem game by any means. It's not even really a full-on harem game, since some characters are only fuck buddies, and Harem isn't even the default path, not really sure there is a default path tbh.
So to answer your question, I believe Lois best fits what you're looking for.